## How to convert binary numbers in two's complement representation from binary system to decimal

### To understand how to convert a binary number in two's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1101 1110, to base ten:

- In a binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so the number is negative.
- Get the binary representation in one's complement, subtract 1 from the binary initial number:

1101 1110 - 1 = 1101 1101 - Get the binary representation of the positive number, flip all the bits in the binary one's complement representation - replace the bits set on 1 with 0-s and the bits set on 0 with 1-s:

!(1101 1101) = 0010 0010 - Write bellow the positive binary number representation in base two, and above each bit that makes up the binary number write the corresponding powers of 2 (numeral base), starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 with exactly one unit:
powers of 2 7 6 5 4 3 2 1 0 number's digits 0 0 1 0 0 0 1 0 - Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then summing up all the terms:

0010 0010_{(2)}=

= 0 * 2^{7}+ 0 * 2^{6}+ 1 * 2^{5}+ 0 * 2^{4}+ 0 * 2^{3}+ 0 * 2^{2}+ 1 * 2^{1}+ 0 * 2^{0}=

= 0 + 0 + 32 + 0 + 0 + 0 + 2 + 0 =

= 32 + 2 =

= 34_{(10)}